Specimen identification system



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SPECIMEN IDENTIFICATION SYSTEM POLY- NOMIAL APPROXI- MATOR POLY" NOMIALAPPROXI- MATOR POLY- NOMIAL p APPROXI- MATOR Ptof APPROXI- MATOR TIMING8 ETECTQR L e R 8: ECTOR fl fof FILTER FILTER 8| FILTER BAND BAND

DETECTOR I 'rot PM/ BAND l April 14, 1964 Filed March 20, 1961 I rT- IFILTE DET I BAND L6 DETECTOR POWER TOTAL' DETECTOR CIRCUIT PCONS @E L'MFILLER p vow DETECTOR F I LgER DETECTOR VOW -CONS April 14, 1964 R.BAKIS SPECIMEN IDENTIFICATION SYSTEM 15 Sheets-Sheet 2 Filed March 20,1961 am 6E mEE.

-FREQUENCY April 14, 1964 R. BAKIS SPECIMEN IDENTIFICATION SYSTEM 15Sheets-Sheet 3 Filed March 20, 1961 um OE m 08 N m lllllll a LOG 1000 +1lllllll so??? E26 o April 14, 1964 R. BAKIS 3,

SPECIMEN IDENTIFICATION SYSTEM Filed March 20, 19 1 15 sheets-sheet eFIG.3c

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wfirzii I m; N; m6 m6 To w ma Yo To --Q To @2523 April 14, 1964 R. BAKlSSPECIMEN IDENTIFICATION SYSTEM 15 Sheets-Sheet 11 Filed March 20, 1961Andi mm-- MI a m =6 Tm 9n ab To w 0 wk Tw MIN n m Q5 Tm wk Pm t $-N 15Sheets-Sheet 12 Filed March 20, 1961 FIG.7

LOW-PASS FILTER BANDPASS FILTER TIME FUNCTION GENERATOR FIG.9

FUNCTION GENERATOR DETECTOR (SQUARE LAW) April 14, 1964 R. BAKISSPECIMEN IDENTIFICATION SYSTEM 15 Sheets-Sheet 13 Filed March 20, 1961 iLIMITER T l E I FIG.1O

SUMMING AMPLIFIER (LIMITED OUTPUT) FIG. 11

INTEGRATOR R. BAKlS SPECIMEN IDENTIFICATION SYSTEM April 14, 1964 FiledMarch 20, 1961 15 Sheets-Sheet 15 E in 50 y. NQNL M J 5%; MEG an l I a z:2 $2 1 mm -w=ou "mafia? an an o m @2228 h max $252; 28 E 5 4% d 1111f!an i mam T T .ll $5025 5525 E I am! :1 H 8N fi r| -.m| xi a m mp GE Q I5 mm PSQEQ @225 United States Patent Ofifice 3,129,287 SPECIMENIDENTIFICATION SYSTEM Raimo Bakis, Ossining, N.Y., assignor toInternational Business Machines Corporation, New York, N.Y., acorporation of New York Filed Mar. 20, 1961, Ser. No. 97,010 13 Claims.(Cl. 1791) This invention relates to methods and apparatus foridentifying specimens making use of techniques of functionapproximation. These techniques are particularly shown with respect to asystem for identifying speech.

The electrical representation of speech that is generated by amicrophone is relatively complicated and presents a difiicultidentification problem. Speech identification devices in the prior artgenerally make use of measurements of the specimen power in variousfrequency bands and compare these measurements with reference powermeasurements. There are many variable speech characteristics introducedby the speaker such as speech speed, pitch, accent and other minorirregularities which adversely affect the operation of these devices. Itis the essence of this invention to provide identification of speechspecimens by analyzing the significant changes of sound in the specimenwhile disregarding other characteristics. This is accomplished bydetermining approximating functions of the specimen data and using thesefunctions, rather than the specimen data itself, to control theidentification of the specimen. The particular approximating functionsthat form the basis of the preferred embodiment of the invention arefunctions of the coefficients of the secondorder polynomials that definethe parabolae that most closely approximate the specimen data.

These techniques of function approximation permit the identification ofirregular specimens without hampering accuracy. When tested with a groupof speakers uttering the ten spoken digits, the system provided acorrect identification for 94% of the specimen utterancesand a rejectindication for 1% of the utterances. An incorrect identification wasmade for 5% of the utterances. None of the speakers used to establishthe system parameters were included in this test.

A text by Claude Merton Wise entitled Applied Phonetics, 1957, is asource of background information in the field of speech. This book ispublished by Prentice-Hall, Inc. and has a Library of Congress CatalogCard No. 57- 9721.

The present invention is embodied in a system for identifying the tenspoken digits based on the vowe content of the specimen, where the Wordvowel is loosely used to refer to the relatively low frequency sounds inthe specimen. In this embodiment, functions of the coefficients of thesecond-order polynomials that define the parabolae that most closelyapproximate logarithmic functions of the ratio of the power in pairs ofbands of frequencies are determined. These functions form the basis foridentifying the specimen. Although the invention is embodied in aspecific speech identification device, it may be seen to be readilyapplicable to the identification of other specimens. In particular, manyphysical phenomena (such as heart-beats, earthquakes, etc.) may bereadily converted into time-varying electrical signals, and theapproximating technique taught herein may be practiced to identifycharacteristics of the phenomena.

One object of this invention is to show methods and apparatus foridentifying a specimen which utilize functions of the specimens whichhave a relatively low dependence upon those characteristics of thespecimen which are relatively low in discriminating value.

A further object is to teach methods and apparatus for identifying aspecimen which utilize functions of integral functions and of parametersderivable from the specimen 3,129,287 Patented Apr. 14, 1964 as thebasis for identification, where the utilized functions have a relativelylow dependence upon the characteristics of 1the specimen which arerelatively low in discriminating va ue.

Another object of this invention is to teach the use of functionapproximation in a specimen identification system.

An object of this invention is to improve specimen identificationsystems by utilizing techniques of polynomial approximation to indicatefunctions of the coefficients of the polynomials which most closelyapproximate various specimen data and providing an indication of theidentity of the specimen based on the functions rather than on thespecimen data itself.

A more particular object is to show the use of techniques of polynomialapproximation to identify a time-varying, analog speech specimen.

A further object is to show a method and apparatus for theidentification of a speech specimen making use of functions of thecoefficients of an approximating polynomial for each of several bands offrequencies contained in the specimen as the basis of theidentification.

The foregoing and other objects, features and advantages of theinvention will be apparent from the following description of a preferredembodiment of a speech identification system.

An analog, time-varying electrical signal, which is representative ofthe speech specimen to be identified, is generated by a microphone. Thissignal is applied to a group of filters, each of which passes acomponent of the signal within a particular band of frequencies. Theoutputs of the filters are applied to square-law detectors whichgenerate signals that are representative of the powers in the variousbands. An additional signal is generated that represents the totalspeech specimen power.

Various pairs of these signals are applied to polynomial approximatorcircuits, each of which generates output signals that are indicative offunctions of the coefficients of a polynomial that approximates thelogarithm of the ratio of the two applied signals. In the embodiment tobe described in detail below, each polynomial approximator developsthree output signals which define a second-order (quadratic) polynomial.The polynomial thus defined is determined by the parabola that mostclosely approximates the shape of the curve representing the logarithmof the ratio of the signals applied to the polynomial approximator.

The output signals from each polynomial approximator are applied to eachof a group of discriminators. One discriminator is required for eachpair of reference Words. Thus forty-five discriminators are required inthe embodiment to be described because ten words (spoken digits) are tobe identified. Each discriminator has a binary output indicating whichspoken digit, of the pair of digits between Which it is designed todiscriminate, most closely approximates the specimen. A decoding matrixutilizes the outputs of the discirirninators to finally determine theidentity of the specimen. A reject circuit provides an indication if thespecimen is not similar to any reference.

Although this invention is embodied in a speech identification systemusing polynomial approximation techniques, it is not meant to be solimited. Many approximating functions are available that would enhancethe identification of a variety of types of specimens, including speechspecimens.

A more particular description of the preferred embodiment of theinvention is based on the accompanying drawings.

In the drawings:

FIGURE 1 is a block diagram of a speech identification embodiment of theinvention.

FIGURES 2a through 2d are diagrams providing data on the spoken digitsone and two.

FIGURE 3 which comprises FIGURES 3a through 3d is a schematic diagram ofa speech identification embodiment of the invention.

FIGURE 4 which comprises FIGURES 4a through 4b is a chart indicating thediscriminator parameters.

FIGURE 5 which comprises FIGURES 5a through 5b is a detailed diagram ofthe decoding matrix shown in abbreviated form in FIGURE 3.

FIGURES 6 through 13 are detailed diagrams of portions of the systemshown in block form in FIGURE 3.

A preferred embodiment of a specimen identification system usingtechniques of polynomial approximation is shown in FIGURE 1. This systemidentifies the ten spoken digits zero through nine. The speech inputspecimen is applied to a microphone 2 which generates a time-varyingelectrical wave form. A group of band circuits 4, each containing one ormore filter and detector circuits 6 and a polynomial approximator 8utilize the microphone output to generate groups of approximatingpolynomial identifying indicia on leads 10. Each filter and detectorcircuit 6 produces an output signal indicative of the amount of power ina particular band of frequencies, as determined by the electricalproperties of the filter. The polynomial approximator circuits 8, inseveral of the band circuits 4, have a second input indicative of thetotal power of the speech signal (P as developed by a total powercircuit 11. One of the band circuits, the band Pg/Pg circuit, does notutilize the total power signal, but rather, has two filter and detectorcircuits 6 because it has been found that the ratio of the powers insome pairs of frequency bands contains highly-discriminating data thatis valuable in the identification of speech. The polynomialapproximators 8 successively perform the following operations on theirinput signals: the ratio of one input signal to the other is determined;the natural logarithm of this ratio is computed; and output indiciadeterminative of the second-order polynomial most closely approximatingthe logarithm of the ratio of the input signals are generated on leads10.

A vowel-consonant circuit 12 containing two filter and detector circuits6 produces output signals indicative of the amount of vowel power andthe amount of consonant power in the speech specimen. This isaccomplished by measuring the power in the relatively low frequencies(vowel) and the power in the relatively high frequencies (consonant).These signals and the total power signal are applied to a timing circuit20 which generates several outputs (shown as a single lead 13) which areapplied to each polynomial approximator 8. These signals are dependentupon the duration of the vowel portion of the speech specimen. While theentire speech specimen could be used as a basis for identifying thespecimen, it has been found that use of only the vowel portion of thespecimen is adequate.

Each polynomial approximator output signal is applied to each of a groupof discriminators 14. These signals are linearly-combined (weighted andadded) to generate a binary output signal on a lead 18. The weightsassigned to each input in each discriminator are determined by the tworeference digits between which the circuit is to discriminate. A binaryoutput is generated which is indicative of the digit that the speechspecimen most closely ap proximates. For example, the 8-9 discriminatorprovides an output indicating whether the input speech specimen moreclosely approximates an 8 or more closely approxi mates 2. 9. Thisdetermination is made by the 8-0 discriminator even if the specimen isneither an 8 or a 9. There are 45 discriminators in the embodiment toprovide discrimination with respect to each pair of digits within theten digits.

A decoding matrix 16 analyzes the binary signals generated by thediscriminators and provides an indication of the identity of thespecimen upon the occurrence of a signal on a lead 15 from the timingcircuit 20.

The basic concept underlying this embodiment is to be described withrespect to the spoken digits one and two. This description couldobviously be extended to cover the remaining eight spoken numerals aswell as any other specimens. The purpose of the following description isto provide an insight into the mathematics underlying the technique andto show a method of ultimately determining the weights to be assigned inthe discriminators. Sample discriminator component values are given indetail with respect to the embodiment but, since they depend upon thereference words, they must be changed if the invention is to be used foridentifying spoken words other than the ten digits or if the ten digitsare spoken by one whose speech is radically different from that of thegroup of speakers who were used in the establishment of the parameters(discriminator weights).

FIGURES 2a-2b are sound spectrograms of the spoken digits one and tworespectively. Time is plotted along the horizontal axis, and frequencyis plotted vertically. The intensity of the spectrogram is indicative ofsignal power, where a dark area indicates a higher power than isindicated by a light area. This method of graphically presenting aspeech specimen is described in detail in a text authored by Ralph K.Potter, George A. Kopp and Harriet C. Green entitled Visible Speech,1947, published by the D. Van Nostrand Co., Inc., New York.

The vertical coordinate is further labelled to indicate the relativefrequency ranges of the two filter and detector circuits 6 (FIG. 1) inthe band Pg/Pg circuit 4. The sample calculations that follow are basedon this circuit but could he obviously extended to include all of theband circuits. The vertical dotted lines encompass the time during whichthe sounds are predominantly vowe These lines are carried across toFIGURES 2c and 20. on a separate sheet, to permit FIGURES 2a and 2c andFIGURES 2b and 2d to be analyzed together. FIGURES 2c and 2d are graphicrepresentations of the relative powers P and P in two bands offrequencies during the vowel portion of the specimen.

The identification of specimens is enhanced by the use of approximatingfunctions of the type that retain the discriminating characteristics ofthe specimens while disregarding other characteristics such as speechirregularities, rate of speaking, loudness, etc.

Functions of the type Pj/Pj are descriptive of the speech soundsproducing them and convenient for use in a specimen identificationsystem. Experiment has shown that, in the embodiment to be described,logarithmic functions of these power ratios provide greaterdiscrimination than is obtained using the power ratios directly. Forthis reason, the vertical scale of the graphs in FIG URES 2c and 2d arelinearly ruled according to the logarithmic function:

The quantity 1 is added to insure that all logarithms are positive. Afactor of 1000 is used to minimize the effect of the added 1.

Since the phonetic content of a speech sound depends not only on theinstantaneous characteristics of the sound at any one instant, but alsoon the way the sound changes, such quantities as the time-derivatives ofthese functions might be considered useful for identification. However,in addition to the significant changes in sound (which the human hears),there are many small irregularities which make the instantaneous valueof the time derivative (of the function) inadequate. Consider the vowelportion of the function P /P for the spoken digit two as plotted inFIGURE 2d. The general trend of the function is an increase with time,corresponding to the changing quality of the a sound as the tongue isgradually lowered from the position it had when the t was beingpronounced. For short periods of time, however, the function actuallydecreases. These short-term fluctuations appear to be of littlesignificance in the identiiication of speech specimens. For this reason,it is expedient to approximate the actual functions with smooth,slowly-varying approximating functions, and to use these functions foridentification.

Three approximating functions are shown in FIGURES 2c and 2d. TheO-order function is a horizontal line having a polynomial expression ofthe type P=C, where C is a constant. The 1st order approximatingfunction is a straight line having a polynomial expression of the type:P=C t+C Similarly, the 2nd-order approximating function is a parabolahaving a polynomial expression of the type P=C t +C t+C A well-knownmethod of approximating functions is to expand them in a series oforthogonal functions, and to truncate this series, using only the firstfew terms. This procedure is described in a reference entitled FourierSeries and Boundary Value Problems, by Ruel V. Churchill, McGraw Hill,1941 in pages 39-41. bet 0c) with i=1, 2, be a series of orthogalfunctions. Then a function f(x) can be approximated (page 4-1, theorem 1of the Churchill reference) in an interval (x x by:

m i wm 1) where:

Filer/(od ai I1 (2) f l i div The particular orthogonal functions usedwith respect to the embodiment to be described are polynomials,orthogonal over the interval (0, 1). The first three of these functionsare:

Since all speakers do not always speak at the same rate, a set offunctions which are orthogonal over the duration of one utterance of aword may not be suitable for another utterance having a differentduration. For this reason the actual duration t, was not used as theargument for the orthogonal functions, but rather a normalized time x.The relationship between x and t is:

These numbers (a a and a if substituted into Equation 1, define theapproximating curves shown in FIG- URES 2c and 2d, where Thus, the afunctions provide information about the gross characteristics of theoriginal functions f(x) while ignoring detailed irregularities which areof less significance for identification. In particular: a is the averagevalue of the function and is indicated as the O-order approximatingfunction; al is related to the slope of the function, or more preciselyto the slope of a straight line approximating the function (1st orderapproximating function); and a is related to the curvature of a parabolaapproximating the function (2nd order approximating function).

If the polynomial approximators 8 shown in FIGURE 1 generated the :1functions, then the only mathematical problem faced would be that ofdetermining the weights a to be used in each discriminator 14 for eachfunction a The polynomial approximators however, generate functions ofthe a; functions, rather than the al functions themselves. This is doneto simplify the structure of the polynomial approximator circuits, atthe expense of complicating the computation of the discriminatorweights. Each polynomial approximator is designed to generate thefollowing three functions I These functions I are related to the afunctions of Equation 5 in that each a functions consists of a linearcombination of one or more I functions. This relationship is made moreobvious if Equations 5 are expanded and x is expressed in terms of taccording to Equation 4.

The linear combinations of the 1 functions that comprise the a functionsare thus:

Since one objective of each discriminator would be to linearly combineits input signals even if :1 functions were applied, there is noincrease in structural complexity introduced by the substitution of I,functions for a functions. This substitution merely affects the relativeweights assigned to the discriminator inputs and has the advantages ofpermitting the use of simple polynomial approximators.

In the following theoretical discussion and numerical example,theoretical weights a are computed. These weights would be applicable tothe discriminator circuits if o functions were generated by thepolynomial approximators. The actual discriminator weights q,(pertaining to the I; functions) are then computed from the theoreticalweights. This procedure is followed because the 11, functions areconsidered to be more nearly distributed as independent random variablesthan are the I and the calculations are simpler for independentvariables. (Independence is defined on pp. 204, 205 of a text entitledAn Introduction to Probability Theory and Its Applications, volume 1, byWilliam Feller, 1957, which is published by John Wiley & Sons, and has aLibrary of Congress Card Number 5740805.)

Each of the eight band circuits 4 provide three output signals, giving atotal of twenty-four signals. Each discriminator 14 receives each of thetwenty-four signals, but the individual weights assigned to each signal.within a group of signals from a single band circuit are independent ofthe individual weights assigned to the signals within other groups. Thisindependence is due to the fact that separate polynomials are defined byeach group of three signals. The following discussion and numericalexample are limited to the procedure for determining the relativeweights to be assigned to a single group of three inputs in a singlediscriminator. The numerical example is limited to the weights assignedto the signals from the band P /P circuit to the 1-2 discriminators.These procedures and examples may obviously be extended to all of theinputs of all of the discriminators.

As previously explained, the first goal of this discussion is to providea procedure for obtaining the weights or, that would be used by adiscriminator in a system where the polynomial approximator providedoutputs representative of the a functions as defined in Equation 8.

The output D(sr) of the discriminator which distinguishes the specimenwith respect to two reference digits s and r may be defined as:

The weights m are determined from a sample of utterances of thereference digits s and r. One simple technique, among the variousavailable techniques, is based on the following assumptions concerning asample of utterances of the reference digits s and r. Consider a (s) anda (r) to be the a, functions generated by the kth utterances of thereference digits s and r, respectively. Assume that, for each of thethree values of i, a (s) and a (r) are random variables with normal(Gaussian) distributions, having means ,u (s) and O) and standarddeviations a (s) and 1 (r). Further assume that the distributions fordifferent values of i are independent. Then for each i there existestimated means no) and AU) d estimated standard deviations 8 (s) and 3-(r) calculated from the sample by:

1 725 /2 i ={m gl nd -fii( )l 1 7L; 1/2 Emmmamr 12 "I k 1 It isnecessary to compute (1 so that the quantity D(sr) from Equation 10 isdifferent for the specimen digits s and r. The function D(sr) has twodistributions, one corresponding to an input specimen s and onecorresponding to an input specimen r, characterized by means ,u (S) andand standard deviations o' (s) and a (r). Since a are assumed to beindependent variables, then the following formulae are valid as shown inchapter IX of the previously-mentioned Feller reference.

ILD(S) z iI -i( The characteristics defined in Equations 13 and 14 areused to determine oq to maximize the probability that the quantity D(sr)in Equation 10 will be larger than a threshold B for an input referencespecimen s and smaller than B for a specimen r. Equation 10 may bealtered to give:

In this case, the problem becomes one of maximizing the probability thatD(sr) is positive for the reference specimen s and negative for r.Rather than maximize this probability, it is sufficient to maximize somemonotonic function of the probability. One such monotonic function isthe distance from the threshold B to the means ,u (s) and ,u (r) dividedby the standard deviations a (s) and a (r). These distances R(s) andR(r) are thus:

This selection of B when substituted into Equations 16 provides:

Thus, if B is chosen according to Equation 17, then R(s) =R(r) and theprobabilities of incorrect identification with respect to the tworeference specimens s and r are equal.

9 10 It is now necessary to maximize either R(s) or R(r). Then accordingto Equations 11 and 12 This maximization problem is difficult to solveexactly. A simplification, however, is obtained by assuming: fi1(1)==1.60607 s =kar 1( 1( 1.223434-1.7g329+0.69126 where k is a constant forall i. Making use of (13), A 14 19 and 20 it can be shown that: 1( )1 I(1.60607) |(1.5O417+l,606O7) ]=O.O147 ECEjI:ILi(-S) i(r) [a (2)]/2[(1.223431.22266) +(1.75329- ms) i I (21) 1.22266) +(0.691261.22266)]=O.282

[2 2 [1+ k] Then according to Equation 27:

a 1.6O6O71.22266 53 Therefore: 1 -01 7+0 282 1/2 1/2 2 501 7' 2i' i' ):l[1 1( )l i( zl: '(m( )Hi'( 1 2 ems) 1 [E WKM] a (22) l )2 i' i' Thosevalues of a; which maximize R(s) make In the sample calculation, onlythree utterances of each 25 digit were considered. In the design of theembodiment, W) a sample of ten utterances of each digit are used. Withbut this larger sample, it is found that: a =-5.17. Similar e htcomputations result in a =3.4() and a =0.617. ri gs) gfiz zgi z g iggggrg giggi i It was assumed in the above discussion that the polyno- 1tt ndition can Writtem mial approxrmators 8 provided a function outputs.a er co These outputs were weighted by corresponding factors 2 a andsummed in a discriminator 14 according to Equa- (s) (T) 2" T tion 10. Aswe have seen, for simplicity, the polynomial 2 :l approximators 8 aredesigned to generate 1 functions (r which are related to the a functionsaccording to Equa- Zen. m( )l sions 9. For this reason, a procedure isrequired for determining the actual discriminator weights q from the Nowthe factor theoretical weights a The following Equation 28 dez u) finesthe relationship between (1 and q i l I 40 D(sr) a-al l i Emil a) m'( )lI Substituting Equation 9 into Equation 28 provides: can be chosenarbitrarily, because multiplying all 0: by

some constant factor does not affect the value of R as oz l +ot (3l +6l(5[ 3 1 +30 it can be seen from Equation 21 that R(s) 1s a homoq111+q2I2(29) geneous function of degrees 0 of 04 Therefore, for s1m- Plicitychoose- Equation 27 may be rewritten as:

z z zw) o* i+ z) o+( 1 2) 1+ 2 2= i 0 o+ 1 1+q2 2 (2 i'[#i( l Thereforeq is related to a; by: Substituting Equation 24 into Equation 23provides qO g(] 3 O+50L 31 qr 1 2 ,u;(S)I-H(T) FLKS) /-i( q =30a e. e1+k e. (r)+tlwe( l The numerical example may now be continued to deter-Substituting Equation 20 into Equation 25 provides i q from a usingEquations 31:

I 1 2 oz =3.40 eam 1%) a =5.17 Since the actual values of a (s) and ,u(r) are not known, 2 the estimated values from Equations 11 and 12 areused. q0=3-403 (5.17)+5(0.617)=22.0 That is, 0: are computed by: q1=6(5-17)*30(0-617)= 49'5 A 1 =30(0.617):18.5 fii( 0) These welghts qpertain only to the input signals to the 1-2 discriminator 14 that weregenerated by the band P /P circuit 4. Since 45 discriminators are usedin the embodiment and since each discriminator has 24 input signals, atotal of 1,080 values for q must be calculated.

The preceding theoretical discussion is the basis for the numericalexample of the computation of a; from the following values of a found byexperiment for the digits 1 and 2 where s refers to the digit 1 and rrefers h 2 In the embodiment, one exception is made. The third tot e lgloutput (I of the band P /P circuits is not used, be-

1( 1-57404 1'5O417 cause it has been found that this signal contributeslittle a (2)=1.22343; 1.75329; 0.69126 to the discrimination of thespeech signal.

7. AN APPARATUS FOR PROVIDING AN INDICATION OF THE IDENTITY OF A CHARACTERISTIC OF A GIVEN FUNCTION OF A VARIABLE COMPRISING IN COMBINATION: FIRST MEANS FOR GENERATING A SECOND FUNCTION OF THE VARIABLE WHICH IS DEPENDENT UPON THE GIVEN FUNCTION; SECOND MEANS RESPONSIVE TO THE OUTPUT OF SAID FIRST MEANS FOR INTEGRATING THE SECOND FUNCTION; MEANS FOR GENERATING A FUNCTION OF THE RATIO OF BOTH THE INTEGRAL AND A PARAMETER DERIVABLE FROM THE GIVEN FUNCTION, SAID RATIO FUNCTION HAVING A REDUCED DEPENDENCE UPON ANOTHER CHARACTERISTIC OF THE GIVEN FUNCTION; AND THIRD MEANS RESPONSIVE TO THE OUTPUT OF SAID SECOND MEANS FOR GENERATING AN INDICATION OF THE IDENTITY OF THE CHARACTERISTIC FROM THE RATIO FUNCTION. 